The circumference of a circle is 25pi, what is the area?
The circumference of a circle is just pi times the diameter of the circle. Therefore, if the circumference of a circle is 25pi, that means the diameter is 25. The area of a circle is pi x r^2, or pi times the radius of the circle squared. Radius is the diameter divided by 2. So our radius is 12.5. Now, the area is pi x 12.5^2 = 490.87 m^2
There is a spring attached horizontally to a fixed wall. At equilibrium, the spring is 10 meters in length. A force of 5 Newtons pushes the spring, causing it to compress. The new length of the spring is 7 meters. What is the spring constant?
Using Hooke's Law, F = -KX, Which F is the force in Newtons, K is the spring constant, and X is the distance the spring is stretched (or compressed), we can find the answer. Plugging in our values from the question, F = 5 N, X = 10m - 7m = 3m. Solving Hooke's law equation for K, we have K = -F/X. So, the spring constant, K = -5/3 = -1.67 N/m.
I really struggle with factoring, what is the best way to go about it?
Well, If you have an X^2 polynomial equation, I focus on the 2nd and 3rd terms in the equation. For instance, let's say I have to factor and solve for X for the equation X^2 - 5X + 6. To factor, let's first focus on the the last term, with is 6. Now right down numbers that are multiples of 6. Now, which of those multiples that you wrote down ADD up to equal 5, which is the second term in our polynomial? Exactly! 2 and 3! So, if we multiply -2 and -3 together, we get 6, and if we add them together, we get -5. So now, to factor the equation, the answer would be (x-2)(x-3).